Vendors: If you did not personally guarantee your debts with the vendors, I would assume you would not be personally liable for outstanding vendor balances. While I hate seeing small companies or mom and pop shops get burned, you don't have to pay back any companies after closing the business in this case. At the very least, you should contact each vendor and return any inventory. While that does not make the vendor whole, at least you are returning that which you have in stock.
Credit cards: There are two ways to determine whether you are personally liable. (1) Call the credit card company and use your Social Security number to look up your account. If your account comes up with that number, it is more likely than not that you are personally liable for that account. (2) Look at the credit card agreement. There will be a clause in the agreement that states you personally guarantee the outstanding balance in the event of default. If the business fails to pay, you and your personal assets become vulnerable.
How do you shut down the business?
If you are fortunate enough not to be personally liable on the debt, then you can walk away.
When the business is the only liable entity, there usually is no reason to file a business bankruptcy. You can file bankruptcy for the business as a "funeral" for it, but a business cannot "discharge" outstanding debts like an individual. This means that the only benefit of filing bankruptcy is to let creditors know the business is insolvent and no one is getting paid.
Though to that end, you do need to officially close the business. Check in the state in which the company is registered because each state has a process to officially closing down sole proprietorships, corporations, limited liability companies and partnerships. This will also stop you from incurring additional state fees associated with your business.